This paper deals with the Optimal scheduling of a microgrid (MG) equipped with dispatchable distributed generators (DGs), renewable generators and electrical storages (batteries). A chance-constrained model is developed to handle normal operation and emergency conditions of MG including DG outage and unwanted islanding. Purchasing reserve from the upstream grid is also considered. Moreover, the uncertainties of loads and renewable resources are incorporated into the model. Furthermore, a novel probabilistic formulation is presented to determine the amount of required reserve in different conditions of MG by introducing separate probability distribution functions (PDFs) for each condition. Accordingly, an index named as the probability of reserve sufficiency (PRS) is introduced. The presented model keeps a given value of PRS in normal and emergency conditions of MG operation. In addition, some controllable variables are added to the chance constraints as an innovative technique to reduce the complexity of the model. Finally, a test microgrid is studied in different case studies and the results are evaluated.

This paper proposes a novel energy hub model for areas using both heat and cold demands that arise due to the major changesin environmental temperature in different periods of the year. The energy demand and the electrical price in a competitiveelectricity market are uncertain with stochastic values which are usually performed by a probability distribution function. Therefore, a stochastic mathematical model representing an Optimal operation of energy hub is based on the objective functionof minimization of energy costs (including electricity and gas). Several constraints such as energy balance, limited capacityof the transformer, air conditioners, gas boilers, absorption chillers, combined heat, and power and battery energy storagesystem are also incorporated into the model to guarantee the required specifications. The high-level algebraic modelingsoftware, general algebraic modeling system has been employed to undertake calculations. Finally, numerical results haveillustrated the efficiency and capability of the proposed models.

This study presents an Optimal framework for the operation of integrated energy systems using demand response programs. The main goal of integrated energy systems is to Optimally supply various demands using different energy carriers such as electricity, heating, and cooling. Considering the power market price, this work investigates the effects of multiple energy storage devices and demand response programs, including the time of use pricing, real-time pricing, and integrated demand response on Optimal operation of energy hub. Moreover, impacts of different optimization methods are evaluated on the Optimal scheduling of multi-carrier energy systems. Maximizing profits of selling electrical energy and minimizing the purchasing cost of input carrier energies are considered as objective functions to indicate bidirectional interchanges of energy hub systems with the power grid. To minimize the generation cost of energy carriers, a new quadratic objective function is also optimized using genetic algorithm. In this study, Optimal operation of the energy hub based on the proposed quadratic objective function is an economic dispatch problem where the purchasing electrical power by the energy hub is considered as a load of the upstream grid. The optimization problem is implemented in the sample energy hub to indicate the effectiveness of different energy storage roles and applied demand response programs in the Optimal operation of energy hub systems.